Nucleation phenomena in electron-hole drop condensation in ultra-pure Ge

  • R. M. Westervelt
  • J. L. Staehli
  • E. E. Haller
  • C. D. Jeffries
Electron-Hole Drops
Part of the Lecture Notes in Physics book series (LNP, volume 57)


By careful measurements and appropriate theory, we are able to observe and explain quantitatively for the first time major aspects of electron-hole drop nucleation phenomena in ultra-pure Ge. The free exciton-drop system above 1.3 K is shown to be always in a metastable state, i.e. dependent upon the history o£ optical excitation. We quantitatively explain the observed luminescence hysteresis and measure the drop surface tension, σ = 2.6 × 10−4 erg cm2 at 2 K. The metastability lifetime is experimentally found to be ≈ 8 × 106 sec. The gas-liquid up-going and down-going threshold curves are measured and explained using an exciton condensation energy ø ≅ 2 meV. The theory also predicts the drop radius and drop concentration as a function of temperature and excitation history.


Drop Size Free Exciton Nucleation Theory Supersaturation Ratio Drop Radius 
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  1. 1).
    For a review of electron-hole drops see Ya Pokrovskii: Phys. Stat. solidi (a) 11 (1972) 385; for a recent review see C. D. Jeffries: Science 189 (1975) 955.Google Scholar
  2. 2).
    T. K. Lo, B. J. Feldman and C. D. Jeffries: Phys. Rev. Letters 31 (1973) 224.Google Scholar
  3. 3).
    Some results of this paper have been briefly published by R. M. Westervelt, J. L. Staehli and E. E. Haller: Bull. Am. Phys. Soc. 20 (1975) 471; J. L. Staehli, R. M. Westervelt and E. E. Haller: Bull. Am. Phys. Soc. 20 (1975) 471.Google Scholar
  4. 4).
    A detailed nucleation theory is given by R. M. Westervelt: Part I, Phys. Stat. sol. (b) 74 (1976) 727; and Part II, Phys. Stat. sol. (b), in press.Google Scholar
  5. 5).
    For a clear review of homogeneous nucleation theory see J. E. McDonald: Am. J. Phys. 30 (1962) 870; also see J. Frenkel: Kinetic Theory of Liquids (Oxford Press, Oxford, 1946).Google Scholar
  6. 6).
    See, e.g. C. Kittel: Thermal Physics (John Wiley, New York, 1969) p. 163. For Ge we use the effective mass m* = 0.335 mo and degeneracy γ = 16, from ref. 2.At temperatures above ≈ 3 K, corrections to eq. 1 become significant, A. Frova, G. A. Thomas, R. E. Miller and E. O. Kane: Phys. Rev. Letters 34 (1975) 1572.Google Scholar
  7. 7).
    An equilibrium treatment of the effects of surface tension has been given by R. N. Silver: Phys. Rev. B11 (1975) 1569.Google Scholar
  8. 8).
    R. Becker and W. Döring: Ann. Physik 24 (1935) 719; R. Becker: Theoy of Heat (Springer-Verlag, New York, 1967), 2nd Edition, p. 239.Google Scholar
  9. 9).
    J. L. Staehli: Phys. Stat. sol. (b) 75, issue 2 (June 1, 1976).Google Scholar
  10. 10).
    R. W. Martin: Solid State Comm. 14 (1974) 369.Google Scholar
  11. 11).
    P. Vashishta: Private communication; P. Vashishta, R. Kalia and K. S. Singwi: Proc. of the Oji Seminar.Google Scholar
  12. 12).
    L. M. Sander, H. B. Shore and L. J. Sham: Phys. Rev. Letters 31 (1973) 533; H. B:uttner and E. Gerlach: J. Phys. C6 (1973) L433; T. M. Rice: Phys. Rev. B9 (1974) 1540; T. L. Reinecke and S. C. Ying: Solid State comm. 14 (1974) 381.Google Scholar
  13. 13).
    The value σ = 1.6 × 10−4 erg cm−2 is estimated by V. S. Bagaev, N. N. Sibeldin, and V. A. Tsvetkov: J.E.T.P. Letters 21 (1975) 80, by measuring the temperature dependence of the concentration of drops by light scattering. However, this paper uses an inaccurate equation (their eq. (2)) and classical nucleation theory. The paper of B. Etienne, C. Benoit â la Guillaume and M. Voos: Phys. Rev. Letters 35 (1975) 536 uses equilibrium theory to estimate an empirical value of (A/σ), where A is the Richardson-Dushman constant, not known for EHD.Google Scholar
  14. 14).
    A. S. Alekseev, T. A. Astemirov, V. S. Bagaev, T. I. Galkina, N. A. Penin, N. N. Sybeldin, V. A. Tsvetkov: Proc. of 12th Intern. Conf. on Physics of Semiconductors, Stuttgart (Teubner, Stuttgart, 1974) p.91.Google Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • R. M. Westervelt
    • 1
  • J. L. Staehli
    • 1
  • E. E. Haller
    • 1
  • C. D. Jeffries
    • 1
  1. 1.University of CaliforniaBerkeleyUSA

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